We investigate holographic complexity for eternal black hole
backgrounds perturbed by shock waves, with both the complexity=action
(CA) and complexity=volume (CV) proposals. We consider Vaidya geometries
describing a thin shell of null fluid with arbitrary energy falling in
from one of the boundaries of a two-sided AdS-Schwarzschild spacetime.
We demonstrate how scrambling and chaos are imprinted in the complexity
of formation and in the full time evolution of complexity via the
switchback effect for light shocks, as well as analogous properties for
heavy ones.